Speaker specifications and Thiele-Small parameters explained
Specifications are useful only when you understand how they were measured and what they do and do not.
Frequency response
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Frequency response shows output level versus frequency under stated measurement conditions.
Before comparing two graphs, check:
- Measurement distance
- Input voltage or power
- On-axis or off-axis angle
- Anechoic, gated, ground-plane, or in-room conditions
- Smoothing
- Whether the graph shows a single sample or an average
A narrow vertical scale can make a response appear smoother than it is.
Sensitivity
Sensitivity describes output for a specified input, usually measured at one metre.
A common rating is:
2.83V @ 1m
The 2.83V convention corresponds to 1 watt only into an 8Ω resistive load. Into 4Ω, 2.83V corresponds to approximately 2 watts.
Do not automatically compare a 1W/1m rating with a 2.83V/1m rating.
Nominal impedance
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Nominal impedance is a simplified label such as 4Ω, 6Ω, or 8Ω. The actual impedance varies with frequency.
A impedance graph shows:
- The minimum magnitude
- Resonance peaks
- The high-frequency rise
- Electrical phase, if available
The minimum impedance and phase angle are more useful to amplifier matching than the nominal value alone.
Power handling
Power handling is not a direct measure of loudness or quality.
A driver may reach one of several limits:
- Voice-coil heating
- Mechanical excursion \(x_{mech}\)
- Suspension stress
- Diaphragm deformation
- Excessive distortion
- Adhesive or former failure
Bass reproduction is often excursion-limited before it is thermally limited.
\(x_{max}\)
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\(x_{max}\) describes linear one-way excursion, but manufacturers do not all define it in the same way.
Some use voice-coil and gap geometry. Others use a specified distortion limit. Compare definitions before comparing numbers.
Volume displacement
A useful low-frequency capability indicator is:
Where \(S_D\) is effective diaphragm area.
A larger volume displacement generally allows greater low-frequency output.
Core Thiele-Small parameters
A basic small-signal low-frequency model can be described using six core parameters:
\(R_E\) : DC voice-coil resistance
The resistance measured at DC (0Hz). It is normally lower than the nominal impedance.
\(f_S\) : Free-air resonance
The resonance frequency of the driver when it is not mounted in an enclosure.
\(Q_{MS}\) : Mechanical Q
Describes mechanical damping around resonance. A high \(Q_{MS}\) means relatively low mechanical loss.
\(Q_{ES}\) : Electrical Q
Describes damping associated with the motor and electrical circuit.
\(Q_{TS}\) : Total Q
The combined electrical and mechanical Q:
Because the damping mechanisms act together, \(Q_{TS}\) is lower than either \(Q_{ES}\) or \(Q_{MS}\).
\(S_D\) : Effective diaphragm area
The effective piston area, not simply the area calculated from the advertised frame diameter.
\(V_{AS}\) : Equivalent compliance volume
The volume of air with the same acoustic compliance as the driver’s suspension.
A low \(V_{AS}\) indicates a relatively stiff suspension when considered with diaphragm area.
Additional useful parameters
- \(M_{MS}\) : Total moving mass, including the air-load [g]
- \(C_{MS}\) : Mechanical compliance [mm/N] (inverse of the stiffness [N/mm])
- \(R_{MS}\) : Mechanical damping resistance [N·s/m]
- \(B\ell\) : Motor force factor [N/A]
- \(L_E\) : Voice-coil inductance [mH]
- \(F_B\) : Enclosure or port tuning frequency [Hz]
- \(F_C\) : Closed-box system resonance [Hz]
- \(Q_{TC}\) : Total Q of a sealed system
- \(V_B\) : Net internal enclosure volume [L]
Important limitation
Thiele-Small parameters describe small-signal behavior mainly around low frequencies. They do not predict cone breakup, high-frequency directivity, cabinet diffraction, thermal compression, or every large-signal nonlinearity.